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A200887 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors. 1
12, 51, 144, 325, 636, 1127, 1856, 2889, 4300, 6171, 8592, 11661, 15484, 20175, 25856, 32657, 40716, 50179, 61200, 73941, 88572, 105271, 124224, 145625, 169676, 196587, 226576, 259869, 296700, 337311, 381952, 430881, 484364, 542675, 606096, 674917 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 2 of A200886.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = (1/3)*n^4 + (7/3)*n^3 + (14/3)*n^2 + (11/3)*n + 1.

Conjectures from Colin Barker, Oct 16 2017: (Start)

G.f.: x*(12 - 9*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = (1+n)^2 * (3+5*n+n^2) / 3.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

EXAMPLE

Some solutions for n=3

..3....1....0....0....3....1....3....1....2....2....0....1....3....1....3....2

..2....1....1....0....1....1....1....0....2....3....3....0....3....3....3....0

..1....3....1....2....2....0....3....1....2....3....3....0....2....3....1....2

..1....3....0....3....3....1....3....2....2....3....2....2....2....0....2....2

CROSSREFS

Sequence in context: A145886 A268351 A166776 * A236770 A115680 A231298

Adjacent sequences:  A200884 A200885 A200886 * A200888 A200889 A200890

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 23 2011

STATUS

approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)